A Conceptual History of Space and Symmetry : From Plato to the Superworld /: From Plato to the Superworld. ([2018])

• Record Type: Book
• Further Information: Note: Pietro Giuseppe Frè.
• Authors: Frè, P
• Contents: Intro; Preface; To my reader; Acknowledgements; Contents; 1 The Episteme; 2 Symmetry and Mathematics; 2.1 Setting the Stage: Symmetry and Beauty; 2.2 Symmetry Principles; 2.3 Geometry and Algebra up to the Birth of Group Theory; 2.4 Galois and the Advent of Group Theory; 2.5 A New Conception of Symmetry; 2.5.1 Conceptual Analysis of Galois Results; 2.5.2 Symmetry After Galois; 2.6 Symmetry, Geometry and Space; 3 How Group Theory Came into Being; 3.1 The Essentials of Group Theory in Modern Parlance; 3.1.1 Examples; 3.1.2 Groups as Transformation Groups; 3.1.3 Representations of a Group 3.2 From Cayley and Sylvester's Matrices to Vector Spaces and Groups: A Long Gestation3.2.1 Cayley and Sylvester: A Short Account of Their Lives; 3.2.2 Matrices in the Middle 1850s; 3.2.3 Cayley and Sylvester: The Invariant Twins; 3.2.4 The Calculus of Operations: Cayley and George Boole; 3.2.5 Grassmann, Peano and the Birth of Vector Spaces; 3.3 Classification of Finite Groups; 3.4 Group Representation and the Unhappy Life of the Man of Two Lemmas; 4 From Crystals to Plato; 4.1 Mathematics and Crystallography; 4.1.1 Crystallographic Groups; 4.1.2 Platonic Groups 4.2 Plato and the Regular Solids4.2.1 The Diophantine Equation that Classifies Finite Rotation Groups; 4.2.2 Case r=2: The Infinite Series of Cyclic Groups mathbbAn; 4.2.3 Case r=3 and Its Solutions; 4.3 A Provisional Conclusion for a Tale Two Thousand Year Long; 4.4 Further Comments About Crystallography; 5 The Long Tale of Lie Groups; 5.1 From Discrete to Continuous Groups; 5.2 Sophus Lie and Felix Klein; 5.2.1 The Spring of 1870 in Paris; 5.2.2 The Erlangen Programme; 5.2.3 Lie Discovers Lie Algebras in Christiania; 5.2.4 Lie and Klein from 1876 to Lie's Death in 1899 5.3 The Tale of Lie Algebras Takes the Lead5.3.1 Levi's Theorem; 5.3.2 Who Was Levi?; 5.4 Killing and Cartan; 5.4.1 The General Form of a Simple Lie Algebra and the Root Systems; 5.5 Dynkin and Coxeter and the Classification of Root Systems; 5.5.1 Dynkin Diagrams; 5.5.2 The Classification Theorem; 5.6 The ADE Classification; 5.7 Comments on the ADE Classification; 6 Hermann Weyl and Representation Theory; 6.1 Conceptual Introduction; 6.1.1 Hermann Weyl; 6.1.2 The Mathematical Way of Thinking, According to Hermann Weyl, with This Author's Comments 6.2 The Basic Notions in Representation Theory6.3 Infinite Dimensional Representations, Hilbert and Quantum Mechanics; 6.3.1 David Hilbert; 6.4 Concluding Remarks on the Idea of Functional Spaces; 7 A Short History of Differential Geometry; 7.1 Conceptual Introduction from a Contemporary Standpoint; 7.1.1 Differentiable Manifolds; 7.2 The Second Stage in the Development of Modern Differential Geometry; 7.3 The Development of Differential Geometry: A Historic Outline; 7.3.1 Gauss Introduces Intrinsic Geometry and Curvilinear Coordinates
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource, illustrations (some colour)
• Subjects: 516.1; Physics; Symmetry (Mathematics) -- History; Geometry -- History; MATHEMATICS / Geometry / General; Science -- Quantum Theory; Science -- Mathematical Physics; Science -- Gravity; Statistical physics; Mathematical physics; Gravity; Mathematical physics; Science -- Physics; History of science; Electronic books
• Languages: English
• ISBNs: 9783319980232; 3319980238
• Related ISBNs: 9783319980225
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (EBSCO, viewed September 19, 2018).; Note: Vendor-supplied metadata.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.